{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "# plt.style.use(\"ggplot\")\n",
    "plt.style.use(\"seaborn-v0_8-whitegrid\")\n",
    "\n",
    "import itertools\n",
    "from itertools import product\n",
    "import sys\n",
    "import pickle\n",
    "sys.path.append('../code')\n",
    "from classification import *\n",
    "from lp import *\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from scipy.spatial import ConvexHull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 95309 entries, 0 to 95308\n",
      "Data columns (total 32 columns):\n",
      " #   Column                                      Non-Null Count  Dtype\n",
      "---  ------                                      --------------  -----\n",
      " 0   readmit_30_days                             95309 non-null  int64\n",
      " 1   black                                       95309 non-null  int64\n",
      " 2   female                                      95309 non-null  int64\n",
      " 3   time_in_hospital                            95309 non-null  int64\n",
      " 4   num_lab_procedures                          95309 non-null  int64\n",
      " 5   num_procedures                              95309 non-null  int64\n",
      " 6   num_medications                             95309 non-null  int64\n",
      " 7   number_diagnoses                            95309 non-null  int64\n",
      " 8   readmit_binary                              95309 non-null  int64\n",
      " 9   age_'30-60 years'                           95309 non-null  bool \n",
      " 10  age_'Over 60 years'                         95309 non-null  bool \n",
      " 11  admission_source_id_Other                   95309 non-null  bool \n",
      " 12  admission_source_id_Referral                95309 non-null  bool \n",
      " 13  medical_specialty_Emergency/Trauma          95309 non-null  bool \n",
      " 14  medical_specialty_Family/GeneralPractice    95309 non-null  bool \n",
      " 15  medical_specialty_InternalMedicine          95309 non-null  bool \n",
      " 16  medical_specialty_Missing                   95309 non-null  bool \n",
      " 17  medical_specialty_Other                     95309 non-null  bool \n",
      " 18  primary_diagnosis_'Musculoskeletal Issues'  95309 non-null  bool \n",
      " 19  primary_diagnosis_'Respiratory Issues'      95309 non-null  bool \n",
      " 20  primary_diagnosis_Diabetes                  95309 non-null  bool \n",
      " 21  primary_diagnosis_Other                     95309 non-null  bool \n",
      " 22  insulin_No                                  95309 non-null  bool \n",
      " 23  insulin_Steady                              95309 non-null  bool \n",
      " 24  insulin_Up                                  95309 non-null  bool \n",
      " 25  change_No                                   95309 non-null  bool \n",
      " 26  diabetesMed_Yes                             95309 non-null  bool \n",
      " 27  medicare_True                               95309 non-null  bool \n",
      " 28  medicaid_True                               95309 non-null  bool \n",
      " 29  had_emergency_True                          95309 non-null  bool \n",
      " 30  had_inpatient_days_True                     95309 non-null  bool \n",
      " 31  had_outpatient_days_True                    95309 non-null  bool \n",
      "dtypes: bool(23), int64(9)\n",
      "memory usage: 8.6 MB\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv(\"../data/diabetes_fairlearn.csv\")\n",
    "\n",
    "Y_columns = [y for y in df.columns if 'admit' in y]\n",
    "G_columns = ['black', 'female']\n",
    "\n",
    "Y_column = 'readmit_binary'\n",
    "G_column = 'female'\n",
    "X_columns = df.columns.drop(Y_columns)\n",
    "X_columns = X_columns.drop(G_column)\n",
    "\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.4669548521126022, 0.47552365949005193, 0.45691697803699993)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_b = df[df[G_column]==1]\n",
    "df_r = df[df[G_column]==0]\n",
    "df[Y_column].mean(), df_b[Y_column].mean(), df_r[Y_column].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5394768594781185, 0.4605231405218815)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_w = df[G_column].mean()\n",
    "p_m = 1 - p_w\n",
    "p_w, p_m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(51417, 43892)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_b.shape[0], df_r.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Point estimate\n",
    "* Figure 9 (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Regression\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.384, e_r=0.384, fairness=0.0\n",
      "[red] e_b=0.386, e_r=0.382, fairness=0.004\n",
      "r-skewed\n",
      "Random Forest\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.393, e_r=0.393, fairness=0.0\n",
      "[red] e_b=0.393, e_r=0.394, fairness=0.001\n",
      "b-skewed\n"
     ]
    }
   ],
   "source": [
    "# G: gender, classification\n",
    "Y_column = 'readmit_binary'\n",
    "G_column = 'female'\n",
    "X_columns = df.columns.drop(Y_columns)\n",
    "X_columns = X_columns.drop(G_column)\n",
    "\n",
    "clf_lr = LogisticRegression(max_iter=1000)\n",
    "\n",
    "print('Logistic Regression')\n",
    "res = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=clf_lr, ratio=None)\n",
    "\n",
    "clf_rf = RandomForestClassifier(n_estimators=500, n_jobs=-1, random_state=42)\n",
    "print('Random Forest')\n",
    "res = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=clf_rf, ratio=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the font properties globally\n",
    "plt.rcParams['font.family'] = 'sans-serif'\n",
    "plt.rcParams['font.sans-serif'] = ['Arial']\n",
    "plt.rcParams['mathtext.fontset'] = 'dejavusans'\n",
    "\n",
    "\n",
    "# Define the range for x and y axes\n",
    "x_range = (0.37, 0.42)\n",
    "y_range = (0.37, 0.42)\n",
    "\n",
    "# Define the grid size\n",
    "grid_size = 0.01\n",
    "\n",
    "# Define the points\n",
    "w_X = [0.393, 0.393]\n",
    "m_X = [0.393, 0.394]\n",
    "\n",
    "# Create the figure and axis\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Set the x and y axis limits\n",
    "ax.set_xlim(x_range)\n",
    "ax.set_ylim(y_range)\n",
    "\n",
    "# Set the grid\n",
    "ax.set_xticks(np.arange(x_range[0], x_range[1] + grid_size, grid_size))\n",
    "ax.set_yticks(np.arange(y_range[0], y_range[1] + grid_size, grid_size))\n",
    "ax.grid(True, linestyle=':', linewidth=0.5)\n",
    "\n",
    "# Increase font size for tick labels\n",
    "ax.tick_params(axis='both', which='major', labelsize=14)\n",
    "\n",
    "# Plot the 45-degree line\n",
    "ax.plot([x_range[0], x_range[1]], [y_range[0], y_range[1]], linewidth=0.5, linestyle='--', color='black')\n",
    "\n",
    "# Plot the points\n",
    "ax.scatter(w_X[0], w_X[1], color='blue', label='Woman-optimal point')\n",
    "ax.scatter(m_X[0], m_X[1], color='red', marker='x', label='Man-optimal point')\n",
    "\n",
    "# Add labels for the points\n",
    "eps = 0.0005\n",
    "ax.text(w_X[0]+2*eps, w_X[1]-5*eps, r'$w_X \\approx m_X$', fontsize=14)\n",
    "# ax.text(m_X[0]-2*eps, m_X[1]+5*eps, r'$m_X$', fontsize=14)\n",
    "\n",
    "# Add a legend\n",
    "legend = ax.legend(frameon=True, facecolor='white', framealpha=1, fontsize=14)\n",
    "# Add labels to the axes\n",
    "ax.set_xlabel(r'$e_w$', fontsize=14)\n",
    "ax.set_ylabel(r'$e_m$', fontsize=14)\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis test\n",
    "* Table 1\n",
    "* See `code/q_test_diabetes_45_logreg.py` and `code/q_test_diabetes_45_rf.py` for details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, 0.1694, 0.0, 0.0, 0.0]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# logistic regression\n",
    "import pickle\n",
    "import numpy as np\n",
    "p_b_list = []\n",
    "\n",
    "for seed in [0,1,2,3,4]:\n",
    "    filename = f'../result/diabetes/test_45_logreg_{seed}_None.pkl'\n",
    "    with open(filename, 'rb') as file:\n",
    "        res = pickle.load(file)\n",
    "\n",
    "    p_b = res['p_b']\n",
    "    p_b_list.append(p_b)\n",
    "\n",
    "print(p_b_list)\n",
    "print(np.median(p_b_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2431, 0.0, 0.0, 0.0437, 0.128]\n",
      "0.0437\n"
     ]
    }
   ],
   "source": [
    "# random forest\n",
    "import pickle\n",
    "import numpy as np\n",
    "p_b_list = []\n",
    "\n",
    "for seed in [0,1,2,3,4]:\n",
    "    filename = f'../result/diabetes/test_45_rf_{seed}_None.pkl'\n",
    "    with open(filename, 'rb') as file:\n",
    "        res = pickle.load(file)\n",
    "\n",
    "    p_b = res['p_b']\n",
    "    p_b_list.append(p_b)\n",
    "\n",
    "print(p_b_list)\n",
    "print(np.median(p_b_list))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frontier estimation\n",
    "* Figure 10 (C) and (D)\n",
    "* See `q_lp_diabetes_gender.py` for details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.016193935939279203,\n",
       " 0.4078241115186838,\n",
       " 0.3916301755794046,\n",
       " 0.38625856115264157,\n",
       " 0.039708137606124114)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seed = 42\n",
    "lmd = 0.0\n",
    "pickle_file_path = f'../result/diabetes/res_LP_diabetes_gender_0.0_42.pkl'\n",
    "\n",
    "# Load the pickle file\n",
    "with open(pickle_file_path, 'rb') as pickle_file:\n",
    "    res = pickle.load(pickle_file)\n",
    "\n",
    "step_size = 5\n",
    "angles_degrees = np.arange(0, 360, step_size)\n",
    "angles_radians = np.radians(angles_degrees)\n",
    "sin_values = np.sin(angles_radians)\n",
    "cos_values = np.cos(angles_radians)\n",
    "\n",
    "obj_list = []\n",
    "for i in range(cos_values.shape[0]):\n",
    "    obj_list.append((cos_values[i], sin_values[i]))\n",
    "\n",
    "num_obj = len(obj_list)\n",
    "e_b_list = res['e_b_list']\n",
    "e_r_list = res['e_r_list']\n",
    "\n",
    "ind_b = np.argmin(e_b_list)\n",
    "ind_r = np.argmin(e_r_list)\n",
    "B_x = e_b_list[ind_b]\n",
    "B_y = e_r_list[ind_b]\n",
    "R_x = e_b_list[ind_r]\n",
    "R_y = e_r_list[ind_r]\n",
    "\n",
    "e_b_temp = 1.0\n",
    "idx = 0\n",
    "for i in range(num_obj):\n",
    "    if e_b_list[i] < e_r_list[i]:\n",
    "        if e_b_temp > e_b_list[i]:\n",
    "            e_b_temp = e_b_list[i]\n",
    "            idx = i\n",
    "e_r_temp = e_r_list[idx]\n",
    "\n",
    "slope = (e_r_temp - R_y) / (e_b_temp - R_x)\n",
    "F_x = (R_y - slope * R_x) / (1 - slope)\n",
    "F_y = F_x\n",
    "F_x - R_x, F_x, R_x, R_y, (F_x - R_x)/F_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration: 0\n",
      "iteration: 1\n",
      "iteration: 2\n",
      "iteration: 3\n",
      "iteration: 4\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.4755313469874264, 0.45689390327940027)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res, y_b = no_info_utilitarian(df, Y_column, G_column, X_columns, seed=seed)\n",
    "u_x = res['e_b']\n",
    "u_y = res['e_r']\n",
    "u_x, u_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = np.array(list(zip(e_b_list, e_r_list)))\n",
    "plt.axes().set_aspect('equal')\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.tick_params(axis='x', which='major', pad=8)\n",
    "\n",
    "# Compute the convex hull\n",
    "hull = ConvexHull(points)\n",
    "\n",
    "# Plot the points\n",
    "# plt.plot(points[:,0], points[:,1], 'x')\n",
    "\n",
    "# Plot the convex hull\n",
    "for simplex in hull.simplices:\n",
    "    plt.plot(points[simplex, 0], points[simplex, 1], 'k-', linewidth=1)\n",
    "\n",
    "# Optionally, you can also fill the convex hull with a color\n",
    "plt.fill(points[hull.vertices,0], points[hull.vertices,1], 'lightblue', alpha=0.4)\n",
    "plt.plot([0, 1], [0, 1], color='gray', linestyle='--')\n",
    "\n",
    "\n",
    "# plt.text(B_x-0.01, B_y+0.01, r'$b_X$', fontsize=12, ha='center', va='center')\n",
    "plt.text(R_x+0.02, R_y-0.01, r'$w_X = m_X$', fontsize=12, ha='center', va='center')\n",
    "plt.plot(B_x, B_y, 'o', color='red')\n",
    "plt.plot(F_x, F_y, 'o', color='red')\n",
    "plt.text(F_x-0.01, F_y+0.01, r'$f_X$', fontsize=12, ha='center', va='center')\n",
    "\n",
    "# no info utilitarian\n",
    "# plt.plot(u_x, u_y, 'o', color='gray')\n",
    "# plt.text(u_x+0.03, u_y-0.03, r'$u_X$', fontsize=12, ha='center', va='center')\n",
    "\n",
    "plt.plot([B_x, F_x], [B_y, F_y], color='red', linewidth=2)\n",
    "\n",
    "plt.xticks(fontsize=12)\n",
    "plt.yticks(fontsize=12)\n",
    "plt.xlabel(r'$e_w$', size=14)\n",
    "plt.ylabel(r'$e_m$', size=14)\n",
    "plt.xlim([0.35, 0.65])\n",
    "plt.ylim([0.35, 0.65])\n",
    "plt.grid(linestyle = \"dashed\")\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x1000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = np.array(list(zip(e_b_list, e_r_list)))\n",
    "\n",
    "from matplotlib.ticker import MultipleLocator, FixedLocator\n",
    "\n",
    "# Setting grid size to 0.02 for both axes\n",
    "plt.axes().set_aspect('equal', adjustable='box')\n",
    "plt.xlim([0.32, 0.50])\n",
    "plt.ylim([0.32, 0.50])\n",
    "ax = plt.gca()\n",
    "ax.xaxis.set_major_locator(MultipleLocator(0.03))\n",
    "ax.yaxis.set_major_locator(MultipleLocator(0.03))\n",
    "# Define your grid start and end points and increments\n",
    "start, end, increment = 0.32, 0.51, 0.03\n",
    "x_positions = y_positions = list(np.arange(start, end, increment))\n",
    "ax.tick_params(axis='x', which='major', pad=8) \n",
    "\n",
    "# Setting the locator for both axes\n",
    "ax = plt.gca()\n",
    "ax.xaxis.set_major_locator(FixedLocator(x_positions))\n",
    "ax.yaxis.set_major_locator(FixedLocator(y_positions))\n",
    "\n",
    "# Compute the convex hull\n",
    "hull = ConvexHull(points)\n",
    "\n",
    "# Plot the points\n",
    "# plt.plot(points[:,0], points[:,1], 'x')\n",
    "\n",
    "# Plot the convex hull\n",
    "for simplex in hull.simplices:\n",
    "    plt.plot(points[simplex, 0], points[simplex, 1], 'k-', linewidth=1)\n",
    "\n",
    "# Optionally, you can also fill the convex hull with a color\n",
    "plt.fill(points[hull.vertices,0], points[hull.vertices,1], 'lightblue', alpha=0.4)\n",
    "plt.plot([0, 1], [0, 1], color='gray', linestyle='--')\n",
    "\n",
    "\n",
    "F_xg = R_x\n",
    "F_yg = R_x\n",
    "\n",
    "plt.plot([R_x, R_x], [R_y, 1.0], linestyle='-', color='blue', linewidth=1)\n",
    "plt.plot([R_x, 1.0], [R_y, R_y], linestyle='-', color='blue', linewidth=1)\n",
    "\n",
    "plt.plot(B_x, B_y, 'o', color='red')\n",
    "plt.plot(F_x, F_y, 'o', color='red')\n",
    "plt.plot(F_xg, F_yg, 'o', color='blue')\n",
    "plt.plot(u_x, u_y, 'o', color='gray')\n",
    "\n",
    "plt.text(u_x+0.01, u_y, r'$u_X$', fontsize=12, ha='center', va='center')\n",
    "plt.text(R_x+0.01, R_y-0.008, r'$w_X = m_X$', fontsize=12, ha='center', va='center')\n",
    "plt.text(F_x-0.005, F_y+0.005, r'$f_X$', fontsize=12, ha='center', va='center')\n",
    "plt.text(F_xg-0.012, F_yg, r'$f_{X,G}$', fontsize=12, ha='center', va='center', color='blue')\n",
    "plt.text(0.455, 0.45, r\"$\\mathcal{E}_{X}$\",fontsize=16, ha='center', va='center')\n",
    "plt.text(R_x+0.02, 0.45, r\"$\\mathcal{E}_{X, G}$\",fontsize=16, ha='center', va='center', color='blue')\n",
    "\n",
    "plt.xlabel(r'$e_w$', size=14)\n",
    "plt.ylabel(r'$e_m$', size=14)\n",
    "plt.xticks(fontsize=12)\n",
    "plt.yticks(fontsize=12)\n",
    "\n",
    "# indifference curve\n",
    "x = np.linspace(0.32, 0.50, 100)\n",
    "y = u_y + (p_w/p_m)*(u_x - x)\n",
    "plt.plot(x, y, color='gray')\n",
    "\n",
    "# arrow\n",
    "plt.arrow(0.49, 0.43, -0.015, -0.015, color='gray')\n",
    "plt.text(0.472, 0.424, r\"$H$\", color='gray', fontsize=16)\n",
    "\n",
    "# FA-frontier\n",
    "plt.plot([B_x, F_x], [B_y, F_y], color='red', linewidth=2)\n",
    "\n",
    "plt.grid(linestyle = \"dashed\")\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Robustness check\n",
    "* Appendix O.6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Point estimates with different models\n",
    "\n",
    "* Try neural nets (NN) and support vector machine (SVM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NN (2-layer)\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.381, e_r=0.379, fairness=0.002\n",
      "[red] e_b=0.381, e_r=0.38, fairness=0.001\n",
      "r-skewed\n",
      "NN (3-layer)\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.384, e_r=0.384, fairness=0.0\n",
      "[red] e_b=0.382, e_r=0.381, fairness=0.001\n",
      "group-balanced\n",
      "SVM\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "no balancing\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.38, e_r=0.377, fairness=0.002\n",
      "[red] e_b=0.381, e_r=0.377, fairness=0.004\n",
      "r-skewed\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neural_network import MLPClassifier\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "mlp = MLPClassifier(hidden_layer_sizes=(32, 32), max_iter=5000, activation='relu', solver='adam', random_state=42,\n",
    "                    early_stopping=True, validation_fraction=0.1, n_iter_no_change=30)\n",
    "print('NN (2-layer)')\n",
    "res_mlp = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=mlp, standardize=True, ratio=None)\n",
    "\n",
    "\n",
    "mlp = MLPClassifier(hidden_layer_sizes=(32, 32, 32), max_iter=5000, activation='relu', solver='adam', random_state=42,\n",
    "                    early_stopping=True, validation_fraction=0.1, n_iter_no_change=30)\n",
    "print('NN (3-layer)')\n",
    "res_mlp = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=mlp, standardize=True, ratio=None)\n",
    "\n",
    "print('SVM')\n",
    "svm = SVC(kernel='rbf', C=1.0, gamma='scale', random_state=42)\n",
    "res_svm = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=svm, standardize=True, ratio=None)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Point estimates with different sample sizes\n",
    "* Estimate group-optimal points varying the size of the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train_frac: 0.7\n",
      "Logistic Regression\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.385, e_r=0.385, fairness=0.0\n",
      "[red] e_b=0.386, e_r=0.382, fairness=0.004\n",
      "r-skewed\n",
      "Random Forest\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.394, e_r=0.393, fairness=0.001\n",
      "[red] e_b=0.393, e_r=0.394, fairness=0.001\n",
      "b-skewed\n",
      "train_frac: 0.8\n",
      "Logistic Regression\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.384, e_r=0.384, fairness=0.0\n",
      "[red] e_b=0.385, e_r=0.381, fairness=0.004\n",
      "r-skewed\n",
      "Random Forest\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.393, e_r=0.391, fairness=0.002\n",
      "[red] e_b=0.393, e_r=0.395, fairness=0.002\n",
      "b-skewed\n",
      "train_frac: 0.9\n",
      "Logistic Regression\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.384, e_r=0.384, fairness=0.0\n",
      "[red] e_b=0.386, e_r=0.382, fairness=0.004\n",
      "r-skewed\n",
      "Random Forest\n",
      "\n",
      "blue: female=1\n",
      "[blue] e_b=0.394, e_r=0.393, fairness=0.0\n",
      "[red] e_b=0.396, e_r=0.394, fairness=0.002\n",
      "r-skewed\n"
     ]
    }
   ],
   "source": [
    "for train_frac in [0.7, 0.8, 0.9]:\n",
    "    print(f'train_frac: {train_frac}')\n",
    "    clf_lr = LogisticRegression(max_iter=1000)\n",
    "\n",
    "    print('Logistic Regression')\n",
    "    res_logreg = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=clf_lr, standardize=True, ratio=None, train_frac=train_frac)\n",
    "\n",
    "    clf_rf = RandomForestClassifier(n_estimators=500, random_state=42, n_jobs=-1)\n",
    "    print('Random Forest')\n",
    "    res_rf = CV_classification(df, Y_column, G_column, X_columns, verbose=True, clf=clf_rf, ratio=None, train_frac=train_frac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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